Surveys in Geophysics

, Volume 40, Issue 1, pp 73–105 | Cite as

The Interpolation of Sparse Geophysical Data

  • Yangkang ChenEmail author
  • Xiaohong Chen
  • Yufeng Wang
  • Shaohuan Zu


Geophysical data interpolation has attracted much attention in the past decades. While a variety of methods are well established for either regularly sampled or irregularly sampled multi-channel data, an effective method for interpolating extremely sparse data samples is still highly demanded. In this paper, we first review the state-of-the-art models for geophysical data interpolation, focusing specifically on the three main types of geophysical interpolation problems, i.e., for irregularly sampled data, regularly sampled data, and sparse geophysical data. We also review the theoretical implications for different interpolation models, i.e., the sparsity-based and the rank-based regularized interpolation approaches. Then, we address the challenge for interpolating highly incomplete low-dimensional data by developing a novel shaping regularization-based inversion algorithm. The interpolation can be formulated as an inverse problem. Due to the ill-posedness of the inversion problem, an effective regularization approach is very necessary. We develop a structural smoothness constraint for regularizing the inverse problem based on the shaping regularization framework. The shaping regularization framework offers a flexible way for constraining the model behavior. The proposed method can be easily applied to interpolate incomplete reflection seismic data, ground penetrating radar data, and earthquake data with large gaps and also to interpolate sparse well-log data for preparing high-fidelity initial model for subsequent full-waveform inversion.


Interpolation Geophysical data processing Inverse problem Sparse data 



We would like to thank Min Bai, Wei Chen, and Yatong Zhou for helpful comments and suggestions on the topic of interpolation. Yangkang Chen would like to thank Sergey Fomel for inspiring discussions on shaping regularization. Yangkang Chen is supported by the Thousand Youth Talents Plan of China, and the starting fund from Zhejiang University. Xiaohong Chen are supported by National Natural Science Foundation of China (Grant No. 41274137), the National Science and Technology of Major Projects of China (Grant No. 2011ZX05019-006), National Engineering Laboratory of Offshore Oil Exploration. Yufeng Wang and Shaohuan Zu are supported by 973 Program of China (Grant No. 2013CB228603), the National Science and Technology Program (Grant No. 2016ZX05010002-002), and the National Natural Science Foundation of China (Grant No. 41174119).


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Yangkang Chen
    • 1
    Email author
  • Xiaohong Chen
    • 2
  • Yufeng Wang
    • 2
  • Shaohuan Zu
    • 2
  1. 1.School of Earth SciencesZhejiang UniversityHangzhouChina
  2. 2.State Key Laboratory of Petroleum Resources and ProspectingChina University of PetroleumBeijingChina

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